### Chapter 4.1: Discrete Conditional Probability

Question 5, Page 150

A coin is tossed three times. Consider the following events

- A: Heads on the ﬁrst toss.
- B: Tails on the second.
- C: Heads on the third toss.
- D: All three outcomes the same (HHH or TTT).
- E: Exactly one head turns up.

#### Which of the following pairs of these events are independent?

- A, B - Independent (Each toss is independent)
- A, D - Dependent (If the second toss is tails, then all three outcomes must be tails for D to occur)
- A, E - Dependent (If heads happens on the first toss, then it can’t occur again for E to happen)
- D, E - Dependent (mutually exclusive)

#### Which of the following triples of these events are independent?

- A, B, C - Independent (Each toss is independent)
- A, B, D - Dependent (mutually exclusive)
- C, D, E - Dependent (mutually exclusive)